Matters Computational: Ideas, Algorithms, Source Code

Matters Computational: Ideas, Algorithms, Source Code
PDF
  • eBook:
    Matters Computational: Ideas, Algorithms, Source Code
  • Author:
    Jörg Arndt
  • Edition:
    1 edition
  • Categories:
  • Data:
    August 23, 2016
  • ISBN:
    3662506629
  • ISBN-13:
    9783662506622
  • Language:
    English
  • Pages:
    980 pages
  • Format:
    PDF

Book Description
This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.

Content

I - Low level algorithms
1. Bit wizardry
2. Permutations and their operations
3. Sorting and searching
4. Data structures

II - Combinatorial generation
6. Combinations
7. Compositions
8. Subsets
9. Mixed radix numbers
10. Permutations
11. Permutations with special properties
12. k-permutations
13. Multisets
14. Gray codes for strings with restrictions
15. Parentheses strings
16. Integer partitions
17. Set partitions
18. Necklaces and Lyndon words
19. Hadamard and conference matrices
20. Searching paths in directed graphs z

III - Fast transforms
21. The Fourier transform
22. Convolution, correlation, and more FFT algorithms
23. The Walsh transform and its relatives
24. The Haar transform
25. The Hartley transform
26. Number theoretic transforms (NTTs)
27. Fast wavelet transforms

IV - Fast arithmetic
28. Fast multiplication and exponentiation
29. Root extraction
30. Iterations for the inversion of a function
31. The AGM, elliptic integrals, and algorithms for computing
32. Logarithm and exponential function
33. Computing the elementary functions with limited resources
34. Numerical evaluation of power series
35. Recurrences and Chebyshev polynomials
36. Hypergeometric series
37. Cyclotomic polynomials, product forms, and continued fractions
38. Synthetic Iterations z

V - Algorithms for nite elds
39. Modular arithmetic and some number theory
40. Binary polynomials
41. Shift registers
42. Binary nite elds: GF(2n)

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